Energy corrugation in atomic-scale friction on graphite revisited by molecular dynamics simulations

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1 At Meh. Sin. (6) ():6 6 DOI.7/s RESEARCH PAPER Energy orrugtion in tomi-sle frition on grphite revisited y moleulr dynmis simultions Xio-Yu Sun, Yi-Zhou Qi Wengen Ouyng Xi-Qio Feng, Qunyng Li, Reeived: 6 July 5 / Revised: August 5 / Aepted: 7 Otoer 5 / Pulished online: Deemer 5 The Chinese Soiety of Theoretil nd Applied Mehnis; Institute of Mehnis, Chinese Ademy of Sienes nd Springer-Verlg Berlin Heidelerg 5 Astrt Although tomi stik slip frition hs een extensively studied sine its first demonstrtion on grphite, the physil understnding of this dissiption-dominted phenomenon is still very limited. In this work, we perform moleulr dynmis (MD) simultions to study the fritionl ehvior of dimond tip sliding over grphite surfe. In ontrst to the ommon wisdom, our MD results suggest tht the energy rrier ssoited lterl sliding (known s energy orrugtion) omes not only from intertion etween the tip nd the top lyer of grphite ut lso from intertions mong the deformed tomi lyers of grphite. Due to the ompetition of these two suentries, frition on grphite n e tuned y ontrolling the reltive dhesion of different interfes. For reltively low tip-grphite dhesion, frition ehves normlly nd inreses with inresing norml lod. However, for reltively high tip-grphite dhesion, frition inreses unusully with deresing norml lod leding to n effetively negtive oeffiient of frition, whih is onsistent with the reent experimentl oservtions on hemilly modified grphite. Our results provide new insight into the physil origins of energy orrugtion in tomi sle frition. Keywords Stik slip frition Energy orrugtion Moleulr dynmis simultion Grphite B Qunyng Li qunyng@tsinghu.edu.n AML nd CNMM, Deprtment of Engineering Mehnis, Tsinghu University, Beijing 8, Chin Deprtment of Engineering Mehnis, Shool of Civil Engineering, Wuhn University, Wuhn 7, Chin Stte Key Lortory of Triology, Tsinghu University, Beijing 8, Chin Introdution Sine its first experimentl demonstrtion on grphite y Mte et l. [], tomi stik slip frition hs een reported to e persistent phenomenon when nnosle tip sliding over rystlline surfes [,]. This interesting ehvior ould e well understood y the theoretil model, whih ws originlly proposed y Prndtl nd Tomlinson [,5] to desrie the surfe diffusion prolem. In the Prndtl nd Tomlinson (PT) model [,5], prtile linerly oupled to spring is drgged forwrd while experiening n intertion fore originting from one-dimensionl periodi energy lndspe. If the vrition mplitude of the energy lndspe is high or the spring onstnt is low enough, instility will our during sliding leding to speil stte where stiking nd slipping pper lterntingly. The PT model hs een shown to e le to qulittively reprodue the experimentl results nd revel mny key hrteristis of the stik slip frition [,6,7]. Despite the suessful pplition of the PT model, severl key spets of tomi stik slip frition, e.g., the physil interprettion of the dmping/dissiption mehnism nd the origin of energy orrugtion, remin unler [,8,9]. Aording to the PT model, the energy rrier ssoited lterl sliding, known s energy orrugtion, will lrgely determine the fritionl resistne of the system. As frition is n interfil proess, the energy orrugtion is ommonly found to e ditted y the energy ssoited with the tipsurfe intertions [,,]. However, reent tomi fore mirosopy (AFM) experiment [] on hemillymodified grphite showed tht frition ould normlly inrese s the ontt lod ws redued resulting in n effetively negtive oeffiient of frition. This peulir frition ehvior ws hypothesized to e used y the lol

2 Energy orrugtion in tomi-sle frition on grphite revisited y moleulr dynmis z y x Grphite Lyer- Lyer- Lyer- Rigid Dimond tip Grphite ( lyers) Tip LJ- Sliding diretion LJ- Fig. Simultionmodel. The tomisti model used in the moleulr dynmis simultions. A shemti showing the dimond grphite system with their speifi intertions delmintion of tomi grphite lyer during retrtion []. Nevertheless, how this delmintion ffets the fritionl resistne nd, furthermore, wht the physil origins of energy for generl sliding proess re, invite more systemti investigtion. In this work, we performed moleulr dynmis (MD) simultions to study the fritionl ehvior of nnosle dimond tip sliding over grphite surfe with vrious degrees of tip-grphite dhesion. The energy vrition during the sliding proess ws nlyzed to identify the physil origins of energy orrugtion ssoited with the fritionl resistne. Our simultion results suggest tht the energy inside the ulk mterils ssoited with pushing the deformed onfigurtion forwrd n lso ply n indispensle role in ontrst to the ommon wisdom. Methods The simultion model is shown in Fig.,. A dimond tip ws used to slide on three-lyered grphite sustrte, nd the resultnt frition nd intertion energy were reorded ontinuously during the simultion. The spheril dimond tip with rdius of R = Å nd height of h = 8Å ws held nd trnslted horizontlly long the grphite surfe. The top few lyers of tip ( Å thik) were ssumed to e rigid while the lower prt ws set s deformle. For ll simultions, the top surfe of the dimond tip hd rystl orienttion long the [] diretion. The grphite sustrte ontined three lyers of grphene, whih hd length of 66 Å nd width of 5 Å. The oordinte system ws hosen suh tht the z-xis is norml to the grphite, the x-xis is long the zigzg diretion nd the y-xis is long the rmhir diretion, shown in Fig.. The whole ottom lyer grphene were fixed to onstrin the rigid-ody motion of the grphite nd the toms t the edges of the top two grphene lyers were lso fixed to void glol sliding mong the lyers. We performed MD simultions using lrge-sle tomi/ moleulr mssively prllel simultor (LAMMPS) []. The C C tomi intertions within the tip or grphite were desried y the mny-ody Tersoff potentil [5,6]. Beuse our work fouses on the elsti nd werless regime, two Lennrd-Jones (LJ) type vn der Wls (vdw) potentils were used for desriing the tomi intertions etween the tip nd grphite lyers (LJ-) nd etween different lyers of grphite (LJ-), respetively. The LJ potentil hs een widely dopted in simulting frition of grphiti mterils nd found to reprodue qulittively onsistent ehvior with experiments [9,,7,8]. In the LJ potentil, the intertion potentil is formulted s U(r) = ε [ (σ/r) (σ/r) 6], where ε is the depth of the potentil well nd σ is the hrteristi distne t whih the potentil is zero. For the LJ potentil etween different lyers of grphite, i.e., LJ-, we used σ =. Å nd ε =.8 MeV [9]. For the intertion etween the tip nd grphite, i.e,. LJ-, we used the LJ prmeters with σ = σ nd ε = λε, where λ is the reltive dhesion ftor representing the rtio of dhesion strength of tip-grphene to grphene-grphene. Aording to the PT model, stik slip frition only ours when the system hs finite loding stiffness [,5]. By vrying the loding stiffness, Sooliu et l. [] experimentlly demonstrted tht sliding n e tuned from stik slip regime to ontinuous sliding regime. In ontrst to the energy dissiption, whih my depend on stiffness of the loding system, temperture ontrol lgorithm nd the msses of the systems, the mximum fritionl resistne during sliding is less ffeted y the system prmeters [7]. Exmining the soure of energy orrugtion help identify the origin of sliding resistne. However, we wnt to note tht the mximum lterl fore vlues reveled in our qusi-stti simultions re upper ounds, nd, in rel sitution, the tip n slip erlier with smller drgging fore when it is driven y finite speed nd t finite temperture. To minimize the impt of therml noise nd etter extrt the sutle energy vritions, we performed qusi-stti simultion t reltively low temperture (. K). For typil simultion, the tip nd the sustrte, where they were fr prt, were firstly relxed to otin the minimum energy onfigurtion y using onjugte grdient method. Then, the tip ws grdully rought into ontt with the sustrte until desired norml lod F n ws rehed. The system ws further thermlly equilirted for ps efore sliding. The lterl sliding ws imposed y inrementlly trnslting the tip long the x-diretion. For eh step, the tip moved. Å followed y therml equilirtion t. K for 5 ps while the rigid prt of the tip ws held fixed. This loding sheme suessfully mimiked qusi-stti sliding s demonstrted y good orreltion etween frition fore nd energy orrugtion.

3 66 X.-Y. Sun et l. Frition (nn) 8 6 Lterl fore (nn) - Lterl fore Potentil energy Low dhesion (λ =.5) Norml lod (nn) Fig. Vrition of frition fore F f s funtion of norml lod. The inset shows the vrition of the lterl fore nd the totl potentil energy of the system s funtions of the lterl displement under norml lod of 8. nn Results nd disussions Frition with low dhesion (λ =.5) We first explored the fritionl ehvior when the tip-grphite dhesion ws reltively wek (λ =.5). Vrition of frition fore F f s funtion of norml lod is given in Fig..Frition fore ws lulted y verging lol pek vlues of lterl fore tre over few tomi periods, nd the negtive nd positive norml fores indite ttrtive nd repulsive intertion etween the tip nd grphite, respetively. Beuse we kept the tip t onstnt height in eh simultion, the norml lod would hnge slightly (depited y the x-unertinty r of the dt points) when the tip moved forwrd. As indited y the urve, frition on grphite inreses monotonilly with the norml lod, whih is qulittively onsistent with the ommon experimentl oservtions on freshly leved grphite []. We lso plot the vrition of the lterl fore nd the totl potentil energy of the system s funtions of the lterl displement under norml lod of 8. nn, s shown in the inset of Fig.. To highlight the osillting feture, the vlues of the potentil energy reported in this pper hve ll een offset to remove the onstnt prt. It n e seen tht the vrition of the potentil energy, or energy orrugtion E totl, ppers to e periodi nd very lose to sinusoidl shpe. By tking the negtive derivtive of U totl with respet to x, i.e., U totl (x)/ x, one n niely reover the lterl fore F L. This good onsisteny etween U totl (x)/ x nd F L demonstrtes tht our system ws indeed good pproximtion of the qusi-stti loding proess where the dynmi nd kineti effets hve een minimized. Sine the frition fore is losely relted to the potentil energy of the system, we lulted the individul omponents of potentil energy nd ompred their vrition Totl potentil energy (ev) trends during the sliding proess. In our simultion model, the totl potentil energy of the system is given y U totl = i= U ti +U tt + i= j i U ij, where U ti is the potentil energy etween the tip nd the i-th-lyer of grphite, U tt is the potentil energy inside the tip, U ij is the potentil energy etween the i-th-lyer, nd j-th-lyer of grphite. To etter understnd the dependene of frition on norml lod s reveled y Fig., we rried out systemti omprison of these ten potentil energy vritions t three typil norml lods, whih n e found in Fig. 7 of the Appendix. From the shemti nd the tomisti simultion results of the deformed onfigurtion shown in Fig., the different omponents of the potentil energy n e essentilly tegorized into two types: the potentil energy ssoited with the sliding interfe U int = i= U ti, nd the potentil energy ssoited with the deformtion inside the ulk mterils U ulk = U tt + i= j i U ij. Figure d present the vrition of U int, U ulk, nd U totl s funtions of the lterl displement t three typil norml lods. It n e seen tht ll the potentil energies re osilltory in phse with similr period of roughly.5 Å, whih well mthes the lttie period of grphite long the zigzg diretion. The results lso indite tht the ontriution from the ulk mterils U ulk is nontrivil t low norml lods nd eomes signifint, or even dominting, t high norml lods. This mens tht the work done y the lterl fore is not only used for driving the tip sliding over the surfe toms ut lso used for pushing the deformed onfigurtion of the sustrte forwrd. When the norml lod inreses, the mplitude of U int only hnges slightly due to inommensurte ontt, ut the mplitude of U ulk eomes more nd more prominent, leding to higher fritionl resistne. To the est of our knowledge, this is the first time tht the onfigurtionl fore due to tomilly osilltory vrition of U ulk ws disussed under the frmework of the PT model.. Frition with strong dhesion (λ = 5) When the tip-grphite dhesion is reltively strong (λ = 5), vrition of frition fore F f s funtion of norml lod is shown in Fig., nd vritions of the lterl fore nd the totl potentil energy of the system s funtions of the lterl displement under typil norml lod re inluded in the inset. Similr to the low dhesion se, the energy orrugtion U totl lso ppers to e periodi nd very lose to sinusoidl shpe. In ddition, y tking the negtive derivtive of U totl nd ompring it with the lterl fore, we gin onfirmed tht the system is in qusi-stti stte. However, in shrp ontrst to the low dhesion se, frition on highly dhesive grphite surfe inreses normlly with deresing norml lod, resulting in negtive slope (or effetive oeffiient of frition). The numeril predi-

4 Energy orrugtion in tomi-sle frition on grphite revisited y moleulr dynmis U ulk U int Frition (nn) 5 Lterl fore (nn) 8 - Lterl fore Potentil energy Totl potentil energy (ev) 5 d Low dhesion (λ=.5) Norml lod = -.9 nn Low dhesion (λ=.5) Norml lod = 7.7 nn Low dhesion (λ=.5) Norml lod = 9. nn Fig. A shemti nd typil tomisti simultion result of the deformed onfigurtion for systems with low dhesion. Vritions of U int, U ulk nd U totl s funtions of the lterl displement t three typil norml lods. F n =.9nN. F n = 7.7nN. d F n = 9.nN tion is onsistent with the reent experimentl oservtion on hemilly-modified grphite [], where the slope of High dhesion (λ = 5) -8-8 Norml lod (nn) Fig. Vrition of frition fore F f s funtion of norml lod. The inset shows the vrition of the lterl fore nd the totl potentil energy of the system s funtions of the lterl displement under norml lod of 6.8nN frition-lod urve ws found to e sensitively dependent on tip-grphite dhesion. Although it ws hypothesized tht the norml inrese of frition ws relted to the lol delmintion of the top grphene lyer [,], it ws still not ler on how this susurfe delmintion ffets fritionl resistne. To revel the physil mehnism of this norml phenomenon, we nlyzed the vritions of the potentil energy in the sme fshion s the low-dhesion se. A shemti nd typil tomisti simultion result of the deformed onfigurtion t high dhesion re shown in Fig. 5. Our simultions gin onfirmed tht the unusul inrese of frition during tip retrtion ws orrelted with the lol delmintion of the top few grphene lyers, s depited in Fig. 5. Similrly, we plot the vrition of U int, U ulk, nd U totl s funtions of the lterl displement t three norml lods in Fig. 5 d (detiled vrition of individul energy omponents n e found in Fig. 8 in the Appendix). It is seen tht, when the norml lod dereses during tip retrtion, the mplitude of the totl energy orrugtion U totl normlly inreses onsistent with the vrition trend of frition. However, y ompring Fig. 5 d with Fig. d, we found tht the key mehnism of inrese of U totl is fundmentlly different for the two ses. In the low dhesion se, the deformtion ours minly vi shering of interfes (oth tip-grphene nd grphene-grphene interfes), nd the lterl fore is trnsmitted ross the interfes diretly. Therefore, oth U int nd U ulk will vry in phse during sliding, nd s result, the inrese of U totl is hieved y inrese of individul omponents. In ontrst, when the tip-grphene dhesion is high, the tomi lyers of grphite n get delminted internlly, s depited in Fig. 5. The lterl fore is minly used for shering long the tip-grphene interfe; ut it is used for rking long the grphene-grphene interfes. Beuse of the different deformtion modes, U int nd U ulk do not neessrily vry in onert, nd there

5 68 X.-Y. Sun et l. U ulk U int Energy orrugtion: U totl = U int (x) + U ulk (x) Sliding diretion U int U ulk x Tip x d - High dhesion (λ=5) Norml lod = -6.8 nn High dhesion (λ=5) Norml lod =.7 nn High dhesion (λ=5) Norml lod = 87. nn Atomi delmintion Fig. 5 A shemti nd typil tomisti simultion result of the deformed onfigurtion for systems with high dhesion. Vritions of U int, U ulk,ndu totl s funtions of the lterl displement t three typil norml lods. F n = 6.8nN. F n =.7nN. d F n = 87.nN is phse differene etween these two omponents. The inrese of U totl with deresing lod t high dhesion is lrgely used y the hnge in phse differene during tip retrtion. For exmple, lthough the mplitude of U int nd Sustrte Fig. 6 A shemti showing generl ontt sliding prolem: the energy rrier (or energy orrugtion) ssoited with sliding the tip forwrd onsists of two prts: U int from the ontt interfe nd U ulk from the ulk mterils; these two omponents n vry with different mplitudes nd phses U ulk do not hnge muh when the norml lod hnges from 87. to 6.8 nn, the mplitude of U totl n inrese lmost % y djusting the phse differene of individul omponents. Conlusions In summry, the fritionl ehvior of dimond tip sliding over grphite surfe with different tip-grphite dhesions ws investigted using MD simultions. It ws found tht the intertion etween the tip nd the top lyer of grphite nd the elsti energy ssoited with the deformtion inside grphite oth ply n importnt role in determining the fritionl ehvior. By ontrolling the reltive strength of tip-grphite dhesion, frition on grphite n e tuned y invoking the ompetition of these two suentries. In roder sense, our simultion results lerly show tht the energy orrugtion ssoited with fritionl sliding omes not only from the interfil intertion ut lso from the deformtion inside the ulk mterils. For generl sliding ontt prolem s shown in Fig. 6, driving fore is needed to overome the interfil resistne s well s to push the deformtion onfigurtion forwrd. The ltter prt n e exhiited s onstnt term t the mrosle or s n extr osilltory onfigurtionl fore t the tomi sle. More importntly, the simultions suggest tht, y djusting its reltive mplitude nd the phse differene with respet to the interfil potentil energy, this osilltory onfigurtionl fore dds rih ingredients to the nnosle frition, whih in turn my offer novel mens for tuning frition t lrger sles. Aknowledgments Qunyng Li would like to thnk the support from the Ntionl Nturl Siene Foundtion of Chin (Grnts 777, 8, 8), the Ntionl Bsi Reserh Progrm of Chin (Grnts CB9, CB9 nd 5CB59), the Tsinghu University Inititive Sientifi Reserh Progrm nd the Thousnd Young Tlents Progrm of Chin. Xio-Yu Sun knowl-

6 Energy orrugtion in tomi-sle frition on grphite revisited y moleulr dynmis edges the finnil support from Chin Postdotorl Siene Foundtion (Grnt M5655). The simultions were performed on the Explorer luster system of Tsinghu Ntionl Lortory for Informtion Siene nd Tehnology. Appendix See Figs. 7 nd Lod = -6.8 nn ΔU t ΔU t ΔU t ΔU ΔU ΔU ΔU ΔU ΔU Lod = -.9 nn ΔU t ΔU t ΔU t ΔU ΔU ΔU ΔU ΔU ΔU Lod =.7 nn ΔU t ΔU t ΔU t ΔU ΔU ΔU ΔU ΔU ΔU Lod = 7.7 nn ΔU t ΔU t ΔU t ΔU ΔU ΔU ΔU ΔU ΔU Lod = 9. nn ΔU t ΔU t ΔU t ΔU ΔU ΔU ΔU ΔU ΔU Fig. 7 Vrition of different omponents of the potentil energy s funtions of the lterl sliding displement with low tip-grphite dhesion. Norml lod t.9 nn. Norml lod t 7.7 nn. Norml lod t 9. nn Lod = 87. nn ΔU t ΔU t ΔU t ΔU ΔU ΔU ΔU ΔU ΔU Fig. 8 Vrition of different omponents of the potentil energy s funtions of the lterl sliding displement with high tip-grphite dhesion. Norml lod t 6.8 nn. Norml lod t.7 nn. Norml lod t 87. nn Referenes. Mte, C.M., Mlellnd, G.M., Erlndsson, R., et l.: Atomi-sle frition of Tungsten tip on grphite surfe. Phys. Rev. Lett. 59, 9 96 (987). Crpik, R.W., Slmeron, M.: Srthing the surfe: fundmentl investigtions of triology with tomi fore mirosopy. Chem. Rev. 97, 6 9 (997)

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